Counting Twin Primes in Residue Classes

By Alex Lemann

Abstract

It is unknown whether there is an infinite number of twin primes, which are primes differing by two. Another question for which an answer is known for primes, but not for the twin primes, is how they are distributed across residue classes. There are generalized arguments that describe when there are more primes that have one remainder when divided by a particular number than another remainder. For example there are more primes 1 mod 10 than 7 mod 10, that is, end in a 1 than a 7 when written in base 10. For twin primes there are similar questions. Are there more twin primes that end in 1 and 3 or twin primes that end in 7 and 9? We develop an experimental metho